my cordeline looks waterlogged in the centre - should I prune it severely half way down the trunk?

Sounds like the growing tip is rotting for some reason. Were it Spring, I'd say yes, chop it down, but this isn't the time of year to do that. On the other hand, I don't see what choice you have, because its dying back anyway. I'd be inclined to put it in a container (if it isn't already), cut back the main stem and keep it in the equivalent of intensive care for the winter - in a very sheltered spot (next to a house wall (preferably a south facing wall) out of the wind, surrounded by other plants/pots etc., and fleece over the top during really cold spells.